diff --git a/logique-programmable/exercices/img/2.1.png b/logique-programmable/exercices/img/2.1.png new file mode 100644 index 0000000..805cf1f Binary files /dev/null and b/logique-programmable/exercices/img/2.1.png differ diff --git a/logique-programmable/exercices/img/2.2.png b/logique-programmable/exercices/img/2.2.png new file mode 100644 index 0000000..0b59ff5 Binary files /dev/null and b/logique-programmable/exercices/img/2.2.png differ diff --git a/logique-programmable/exercices/img/2.3.png b/logique-programmable/exercices/img/2.3.png new file mode 100644 index 0000000..14f019e Binary files /dev/null and b/logique-programmable/exercices/img/2.3.png differ diff --git a/logique-programmable/exercices/img/2021-09-14-212219_357x187_scrot.png b/logique-programmable/exercices/img/2021-09-14-212219_357x187_scrot.png new file mode 100644 index 0000000..a5cb414 Binary files /dev/null and b/logique-programmable/exercices/img/2021-09-14-212219_357x187_scrot.png differ diff --git a/logique-programmable/exercices/main.tex b/logique-programmable/exercices/main.tex new file mode 100644 index 0000000..35fdf4f --- /dev/null +++ b/logique-programmable/exercices/main.tex @@ -0,0 +1,107 @@ +\documentclass[a4paper,french,12pt]{article} + +\title{Logique Programmable --- Exercices} +\author{Catherine MARECHAL --- \href{mailto:catherine.marechal@efrei.fr}{\nolinkurl{catherine.marechal@efrei.fr}}} +\date{Dernière compilation~: \today{} à \currenttime} + +\usepackage{../../cours} + +\begin{document} + +\maketitle + +\section{Simplification des fonctions logiques} + \subsection{Exercice 1} + \subsection{Exercice 2} + \subsection{Exercice 3} + \subsection{Exercice 4} + \subsection{Exercice 5} + \subsection{Exercice 6} + \subsection{Exercice 7} + +\section{Circuits de logique combinatoire} + \subsection{Exercice 1} + + \includegraphics[width=0.6\linewidth]{./img/2.1.png} + + \subsection{Exercice 2} + + a/ Élaborer l'équation logique $F(S_1,S_0,C,a,b)$ du circuit ci-dessous. + + \includegraphics[width=\linewidth]{./img/2.2.png} + + \begin{equation*} + F = \bar{c} + \overline{S_0}(ab + \bar{a}\bar{b}S_1) + \end{equation*} + + b/ Compléter le tableau suivant pour C = 0~: + + $F = \bar{c}$ + + \begin{tabularx}{0.8\linewidth}{cccY} + \toprule + C & $S_1$ & $S_0$ & $F(a,b)$ \\ + \midrule + 0 & 0 & 0 & 1 \\ + 0 & 0 & 1 & 1 \\ + 0 & 1 & 0 & 1 \\ + 0 & 1 & 1 & 1 \\ + \bottomrule + \end{tabularx} + + c/ Compléter le tableau suivant pour C = 1~: + + $F = \overline{S_0}(ab + \bar{a}\bar{b}S_1)$ + + \begin{tabularx}{0.8\linewidth}{cccY} + \toprule + C & $S_1$ & $S_0$ & $F(a,b)$ \\ + \midrule + 1 & 0 & 0 & $ab$ \\ + 1 & 0 & 1 & 0 \\ + 1 & 1 & 0 & $ab + \bar{a}\bar{b}$ \\ + 1 & 1 & 1 & 0 \\ + \bottomrule + \end{tabularx} + + \subsection{Exercice 3} + + Soit le schéma de $H(A,B,C,D)$ utilisant un multiplexeur à 3 entrées d'adresse. + + \includegraphics[width=0.6\linewidth]{./img/2.3.png} + + a/ Donner la table de vérité de la fonction $H$. + + \begin{tabularx}{0.7\linewidth}{X|Y|YYY|Y} + \toprule + & D & C & B & A & H \\ + \midrule + 0 & 0 & 0 & 0 & 0 & 0 \\ + 1 & 0 & 0 & 0 & 1 & 0 \\ + 2 & 0 & 0 & 1 & 0 & 0 \\ + 3 & 0 & 0 & 1 & 1 & 0 \\ + 4 & 0 & 1 & 0 & 0 & 0 \\ + 5 & 0 & 1 & 0 & 1 & 0 \\ + 6 & 0 & 1 & 1 & 0 & 1 \\ + 7 & 0 & 1 & 1 & 1 & 0 \\ + \midrule + 8 (0) & 1 & 0 & 0 & 0 & 0 \\ + 9 (1) & 1 & 0 & 0 & 1 & 0 \\ + 10 (2) & 1 & 0 & 1 & 0 & 1 \\ + 11 (3) & 1 & 0 & 1 & 1 & 1 \\ + 12 (4) & 1 & 1 & 0 & 0 & 0 \\ + 13 (5) & 1 & 1 & 0 & 1 & 1 \\ + 14 (6) & 1 & 1 & 1 & 0 & 1 \\ + 15 (7) & 1 & 1 & 1 & 1 & 0 \\ + \bottomrule + \end{tabularx} + + b/ Exprimer $H(A,B,C,D)$ sous la forme disjonctive. + + \begin{equation*} + H(A,B,C,D) = \bar{A}BC\bar{D} + \bar{A}B\bar{C}D + AB\bar{C}D + A\bar{B}CD + \bar{A}BCD + \end{equation*} + + \subsection{Exercice 4} + +\end{document}